Parikshit's Corner

The Glass Theory

2010-06-17T15:11:00.000+05:30

People have used a simple glass and some water to define certain kinds of people. Most motivational speakers or books describe an optimist as someone who finds a glass half-filled with water as half-full as opposed to a pessimist who finds it to be half-empty. There is no objection to the above definitions but they do not describe the complete set of optimists and pessimists.

Consider that a glass is partially filled with water (or any other drink you want). An optimist will see even a 10% filled glass as somewhat filled rather than somewhat empty. (Assuming the guy is not thirsty). On the other hand, a pessimist will see a 90% filled glass as somewhat empty. The genius is always the entrepreneur who, even after getting an empty glass, will see the glass as an opportunity to be filled and will promptly fill it.

Footnote – A person who can discern that a half-filled glass is both half-empty and half-full will surely be an engineer ;-).

Fermat's Last Theorem

2009-05-14T14:59:00.009+05:30

(In continuation, if you could call this continuity, I am writing about a book that I had bought a long time ago but have read only recently. This is about one of the longest unsolved (until recently) riddles of mathematics - Fermat's Last Theorem)

During my schooldays, whenever someone asked which was my favorite subject, I always answered - Maths. But over the course of my studies, especially during engineering, Maths just became a subject one studied because one has to clear it with no particular interest in its complexities. But during the schooldays, Maths was beautiful - beautiful in its simplicity, it was marvellous - in its ability to make you wonder.

Over the years, I have read many books by eminent scientists about the universe, the subatomic, the laws, relativity and everything written for us the lesser mortals to understand and get the picture of what all is about. But, I think, this book by Simon Singh - Fermat's Last Theorem, is one of its kind which gives an insight into the most difficult problem in mathematics for over 3 centuries!!

Let me first state the theorem which in itself looks so innocuous that it is hard to believe that it could haunt the finest brains in the world for over 3 centuries. We all know the Pythagoras Theorem:

For any right angled triangle, the sum of the squares of the two perpendicular sides is equal to the square of the hypotenuse. If z is the hypotenuse and x, y are the two sides, we write it as:

x² + y² = z²

It is also known that, the above equation has integer solutions. For example, the numbers 3,4 and 5 satisfy this equations as 9 + 16 = 25.

Now, Fermat's Last Theorem simply states that:
The equation xⁿ + yⁿ = zⁿ has no integer solutions for n > 2.

Although the proof for this simple looking equation done by Andrew Wiles is over 250 pages using the most complex mathematical tools developed in the last century, Fermat had mentioned this theorem on the margin of one of his books and adding that he has a marvellous proof of the theorem but the space is too small for it!!

I liked the books mainly because it takes you on a thrilling journey of mathematics (number theory) starting from the ancient days of Pythagoras to Euclid to the medival times of Euler and Fermat to modern times of Wiles. You get to travel from ancient Greece to Egypt to medieval Europe to the world of today. The book covers interesting anecdotes from the lives of the greatest mathematicians the world has ever seen - their successes, their failures, their moments of pure genius, while not diverting from the central protagonist - Mathematics.

Not only that the mathematical concepts are explained so lucidly that a layman can understand, there are a number of riddles and problems interspersed throughout which made me to think, to smile, to take myself back to the old schooldays. This book made me fall back in love with my favorite subject again!!

I would strongly recommend this book to anybody who has ever been in love with Mathematics.

Marvin - The Paranoid Android

2008-10-01T02:56:00.004+05:30

For some time now, I have been thinking of writing about some of my favorite fictional characters. It finally needed a sleepless night to get that going. I am starting here. Many more would follow (depending on my sleep cycles).

One of my favouritest series is the Hitchhiker's Guide trilogy (in five parts as often described). It is a unique science-fiction-comedy and truly one of its kind. A restaurant at the end of the universe where (in terms of timeline) anyone could dine (timetravel is obvious) and enjoy the cosmic fireworks of the ending universe. Payment is not an issue because, one can go back in the past and put a penny in their bank account which will get compounded to enough money till the end of the universe!! A spaceship which works using an improbability drive (the probability of anything at any point in space is almost zero and hence the improbability is infinite!!). Of all the books which search for an answer, the whole series is devoted to the Ultimate Question (the answer to which is ofcourse 42!!).

In between all these are intertwined many characters across the universe but my favorite is Marvin (an android) who has a brain the size of a planet (50,000 more intelligent than a human and 30 billion times than a mattress!!) and the problem with his existence is that there is no task big enough (in the universe) that could even utilize a fraction of his brain. He is just splendidly frustrated all the time. Out of all the crazy characters, he (also crazy ofcourse) is the only sane one who just knows that he has brain but not using it.

Now, ofcourse none of us has a brain of the size of a planet (most don't even have it the size of an ant's brain) but none of us actually realize that we also do not use it most of the times. This is a stark reality which only Marvin has been able to realize.

Oops and now I realize that I did not use mine much for the last 20 mins or so!!

Life Is Like That

2008-09-16T23:31:00.001+05:30

(From my older blog page)

“Damn you fool #%$&....”, I muttered under my breath as the driver in front of me changed his lane without an indicator and I had to almost stand on the brakes. This was nothing new for anyone driving in Delhi and nothing new for my day's beginning. Most of my days start by cursing on the road and this sets the tempo for the diurnal events to follow. But that January morning was different. The law of averages is a law after all.

“Damn you fool #%$&....”, I muttered under my breath as the driver in front of me changed his lane without an indicator and I had to almost stand on the brakes. Nothing new, I changed back to the second gear, pressed the gas and passed the driver giving him hideous looks which he accepted quite thankfully.

On the turn to the Greater Noida Expressway, there is always a bunch of hitchhikers needing lift to Greater Noida. They contribute equally to my cursing lessons by coming in front of my car to get A lift and I don't even go to Greater Noida. I just take the service lane to my office. On that January morning, I had decided that I will just knock over anyone who comes in my way. I was in the greatest of moods, you know.

As I somehow managed to take the free left (as the DTC bus felt kind enough to spare me some space), I did not see the crowd of hitchhikers. May be, nature had decided to let them know of my mood. It was 10 in the morning and still no sun. It was all gloomy with dense fog dampening the spirits and the vision. I just thought, maybe I cannot see them because of the fog and they must be lurking in somewhere to jump in front of my car. But I had decided, come what may, I am not stopping. And aren't there lessons to be learnt everywhere; darkest of fears keep lurking in the deepest corners of your mind and sometimes you have to just knock them over.

As I completed the turn, I did not know but I stopped after a few metres. She came to my window and said, “Can I get a lift to Greater Noida?” and someone somewhere said “Yes”. It took me an eternity to comprehend that I said that and by that time she was comfortably sitting next to me singing melodiously in my ears. Someone somewhere started a screeching alarm and I regained my senses only to know that she was thanking me. I just smiled at myself and sped off. And the problem was she was also smiling.

I kept driving, cursing myself why did I stop (this is a new lesson) and she kept smiling. Life tries to teach you but what if you are dumb. She kept smiling, making me more uncomfortable. Someone has said, girls are evil and that seemed to be true as they can just torture you with their smile. I started a conversation as I saw Chetan Bhagat's latest novel in her bag which I had already read.

“I hope you are not God as in that novel.”

She smiled again and I got tortured again.

“Well, of course not, and I haven't read that book.”

I cursed myself again.

“I am sorry and its a nice book.”

“I am no God, but I can forgive you.” She smiled again. But this time, I smiled too and this broke the ice. We went on talking and I kept on stretching the miles. No one would have ever driven so slow on the 8-lane Expressway. But physics is no joke and we neared Greater Noida. We promised to meet sometime and as we reached her destination, she looked into my eyes, a deep penetrating look. And then she just got off and left. The fog was gone and the sun shone brightly.

Life gives you everything – the good, the bad and the ugly but its you who have to grab when it gives you the good. As I parked in front of my office, I cursed myself, “She was standing right there. If only I had stopped”.

The Last Wednesday?

2008-09-10T01:25:00.000+05:30

For the last couple of days, the news channels are flooded by the news speculating the end of universe. A good bunch of physicists at CERN have created a monumentally expensive machine ($7 billion!!) somewhere under the French-Swiss border to simulate the BIG BANG. It has come to my diminished knowledge that of the many different objectives of this experiment, one is to find a particular partical called God-particle (or for me just a god-forsaken particle) which would prove the ambiguity about the mass of the universe.

I am nowhere near understanding the pros and cons of such an experiment but I read that the skeptics have predicted absolutely devastating results if the experiment goes haywire. The experiment might create a black hole and then obviously everything would get sucked into the black hole!!

I do not know how the black hole would like to gobble all of us but even if it stops to relish the taste, everything would go almost in a flash - just like that - suddenly. Wouldn't it be a more convinient way of ending everything? Nobody would know anything. Otherwise the way we are going, the way civilization is degenerating, the way there are wars, the way there are calamities, the way every natural resource is getting depleted, the way Mother Nature is reciprocating, the way we are losing control of everything and the way we still believe that we have everything under human control; there is nothing else other than more suffering for everyone.

Just to be clear I am not a pessimist and I strongly believe in life and the will to live :) but I am just pondering over what if it actually is the last Wednesday? How clever of the physicists who are conducting this experiment that even if the experiment fails, all of us would atleast get the chance to see a real black hole ;) Its a real win-win situation for the physicists because if they succed, they will get all the glory but if they fail nobody will be there to complain.